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数感练习：在分数与小数表示间切换（有限与循环）

数感练习：在分数与小数表示间切换（有限与循环）
几何画板及绘图内容加载中，请稍等……
2023-05-08 16:37
函数数列变换几何作图滑块动画
所属专题 Bruchzahlen in endliche Dezimalzahlen umrechnen
这个 GeoGebra 范例演示如何在同一有理数的不同表示之间进行切换，并让学生判断分数与（有限或循环）小数形式的对应关系。核心数学概念包括：有理数、分数表示、有限小数、循环小数、以及分数与小数之间的等值对应（强调“表示形式”而非计算套路）。作图/实现要点可从构造摘要提炼：使用 Shuffle 进行题目或对象的随机化，利用 Vector、Segment、Join、Polygon 生成界面与可视元素（如分段图形或交互区域），用 Element 与 If 控制对象选择与条件显示，配合 Text 输出数值与提示；同时借助 Zip、Count/ countCorrect、correct、button1 等对象/计数变量实现练习生成、作答与正确性统计。适合5-6年级用于课堂练习或复习“分数—小数等值转换”的基础概念。

GeoGebra 命令及参数

  1. Shuffle(1…Length[exercises]) → randomIndices, {10, 15, 57, 19, 32, 35, 23, 52, 54, 56, 13, 46, 3, 33, 21, 37, 16, 17, 44, 29, 48, 51, 53, 38, 1, 18, 28, 50, 11, 41, 25, 40, 45, 39, 4, 2, 36, 55, 6, 58, 20, 22, 34, 7, 43, 31, 14, 49, 26, 12, 42, 47, 24, 8, 5, 30, 27, 9}
  2. Zip(ParseToNumber[aa], aa, exercises) → exercisesNums
  3. Vector(A, B) → u
  4. Segment((0, a), (0, (-a))) → f
  5. Segment((10, b), (10, (-b))) → g
  6. Join({{100}, Shuffle[Sequence[Random[5, 95], i, 1, 100]]}) → randomNos
  7. Element(exercisesNums, randomIndices(1 + Mod[count, 58])) → num
  8. Polygon((Max[0, (100 * num / 10) - 0.5], -0.3), (Min[10, (100 * num / 10) + 0.5], -0.3), (Min[10, (100 * num / 10) + 0.5], 0.3), (Max[0, (100 * num / 10) - 0.5], 0.3)) → q1, h, i, j, k
  9. Segment((0, 0), (0.1, 0)) → P0
  10. Segment((0.1, 0), (0.2, 0)) → P1
  11. Segment((0.2, 0), (0.3, 0)) → P2
  12. Segment((0.3, 0), (0.4, 0)) → P3
  13. Segment((0.4, 0), (0.5, 0)) → P4
  14. Segment((0.5, 0), (0.6, 0)) → P5
  15. Segment((0.6, 0), (0.7, 0)) → P6
  16. Segment((0.7, 0), (0.8, 0)) → P7
  17. Segment((0.8, 0), (0.9, 0)) → P8
  18. Segment((0.9, 0), (1, 0)) → P9
  19. Segment((1, 0), (1.1, 0)) → P10
  20. Segment((1.1, 0), (1.2, 0)) → P11
  21. Segment((1.2, 0), (1.3, 0)) → P12
  22. Segment((1.3, 0), (1.4, 0)) → P13
  23. Segment((1.4, 0), (1.5, 0)) → P14
  24. Segment((1.5, 0), (1.6, 0)) → P15
  25. Segment((1.6, 0), (1.7, 0)) → P16
  26. Segment((1.7, 0), (1.8, 0)) → P17
  27. Segment((1.8, 0), (1.9, 0)) → P18
  28. Segment((1.9, 0), (2, 0)) → P19
  29. Segment((2, 0), (2.1, 0)) → P20
  30. Segment((2.1, 0), (2.2, 0)) → P21
  31. Segment((2.2, 0), (2.3, 0)) → P22
  32. Segment((2.3, 0), (2.4, 0)) → P23
  33. Segment((2.4, 0), (2.5, 0)) → P24
  34. Segment((2.5, 0), (2.6, 0)) → P25
  35. Segment((2.6, 0), (2.7, 0)) → P26
  36. Segment((2.7, 0), (2.8, 0)) → P27
  37. Segment((2.8, 0), (2.9, 0)) → P28
  38. Segment((2.9, 0), (3, 0)) → P29
  39. Segment((3, 0), (3.1, 0)) → P30
  40. Segment((3.1, 0), (3.2, 0)) → P31
  41. Segment((3.2, 0), (3.3, 0)) → P32
  42. Segment((3.3, 0), (3.4, 0)) → P33
  43. Segment((3.4, 0), (3.5, 0)) → P34
  44. Segment((3.5, 0), (3.6, 0)) → P35
  45. Segment((3.6, 0), (3.7, 0)) → P36
  46. Segment((3.7, 0), (3.8, 0)) → P37
  47. Segment((3.8, 0), (3.9, 0)) → P38
  48. Segment((3.9, 0), (4, 0)) → P39
  49. Segment((4, 0), (4.1, 0)) → P40
  50. Segment((4.1, 0), (4.2, 0)) → P41
  51. Segment((4.2, 0), (4.3, 0)) → P42
  52. Segment((4.3, 0), (4.4, 0)) → P43
  53. Segment((4.4, 0), (4.5, 0)) → P44
  54. Segment((4.5, 0), (4.6, 0)) → P45
  55. Segment((4.6, 0), (4.7, 0)) → P46
  56. Segment((4.7, 0), (4.8, 0)) → P47
  57. Segment((4.9, 0), (5, 0)) → P49
  58. Segment((5, 0), (5.1, 0)) → P50
  59. Segment((5.1, 0), (5.2, 0)) → P51
  60. Segment((5.2, 0), (5.3, 0)) → P52
  61. Segment((5.3, 0), (5.4, 0)) → P53
  62. Segment((5.4, 0), (5.5, 0)) → P54
  63. Segment((5.5, 0), (5.6, 0)) → P55
  64. Segment((5.6, 0), (5.7, 0)) → P56
  65. Segment((5.7, 0), (5.8, 0)) → P57
  66. Segment((5.8, 0), (5.9, 0)) → P58
  67. Segment((5.9, 0), (6, 0)) → P59
  68. Segment((6, 0), (6.1, 0)) → P60
  69. Segment((6.1, 0), (6.2, 0)) → P61
  70. Segment((6.2, 0), (6.3, 0)) → P62
  71. Segment((6.3, 0), (6.4, 0)) → P63
  72. Segment((6.4, 0), (6.5, 0)) → P64
  73. Segment((6.5, 0), (6.6, 0)) → P65
  74. Segment((6.6, 0), (6.7, 0)) → P66
  75. Segment((6.7, 0), (6.8, 0)) → P67
  76. Segment((6.8, 0), (6.9, 0)) → P68
  77. Segment((6.9, 0), (7, 0)) → P69
  78. Segment((7, 0), (7.1, 0)) → P70
  79. Segment((7.1, 0), (7.2, 0)) → P71
  80. Segment((7.2, 0), (7.3, 0)) → P72
  81. Segment((7.3, 0), (7.4, 0)) → P73
  82. Segment((7.4, 0), (7.5, 0)) → P74
  83. Segment((7.5, 0), (7.6, 0)) → P75
  84. Segment((7.6, 0), (7.7, 0)) → P76
  85. Segment((7.7, 0), (7.8, 0)) → P77
  86. Segment((7.8, 0), (7.9, 0)) → P78
  87. Segment((7.9, 0), (8, 0)) → P79
  88. Segment((8, 0), (8.1, 0)) → P80
  89. Segment((8.1, 0), (8.2, 0)) → P81
  90. Segment((8.2, 0), (8.3, 0)) → P82
  91. Segment((8.3, 0), (8.4, 0)) → P83
  92. Segment((8.4, 0), (8.5, 0)) → P84
  93. Segment((8.5, 0), (8.6, 0)) → P85
  94. Segment((8.6, 0), (8.7, 0)) → P86
  95. Segment((8.7, 0), (8.8, 0)) → P87
  96. Segment((8.8, 0), (8.9, 0)) → P88
  97. Segment((8.9, 0), (9, 0)) → P89
  98. Segment((9, 0), (9.1, 0)) → P90
  99. Segment((9.1, 0), (9.2, 0)) → P91
  100. Segment((9.2, 0), (9.3, 0)) → P92
  101. Segment((9.3, 0), (9.4, 0)) → P93
  102. Segment((9.4, 0), (9.5, 0)) → P94
  103. Segment((9.5, 0), (9.6, 0)) → P95
  104. Segment((9.6, 0), (9.7, 0)) → P96
  105. Segment((9.7, 0), (9.8, 0)) → P97
  106. Segment((9.8, 0), (9.9, 0)) → P98
  107. Segment((9.9, 0), (10, 0)) → P99
  108. Segment((10, 0), (10.1, 0)) → P100
  109. Segment((4.8, 0), (4.9, 0)) → P48
  110. If(floor(barometer / 2) + 1 ≥ 10, 10, floor(barometer / 2) + 1) → colorIndex
  111. Polygon((-1, -8), (17, -8), (17, 5), (-1, 5)) → canvas, l, m, n, p
  112. Text("\textsf{" + (If[Mod[1 + Mod[count, 58], 2] ≟ 1, (("\[" * numFracLatex) * "\]"), numDec]) + "}", ((100 * num / 10), If[Mod[1 + Mod[count, 58], 2] ≟ 1, -0.95, -0.75]), true, true, 0, 0) → text6
  113. Vector(((100 * num / 10), -0.4), ((100 * num / 10), 0)) → v

AI 绘图提示语参考

绘制一个用于分数与小数转换练习的交互式数轴。数轴从0到4，被细分为0.1单位的等长小段，形成连续的刻度线。在数轴上方，随机显示一个分数（如3/4），并在数轴下方用高亮色块标出该分数对应的小数位置，色块宽度为0.1单位，覆盖在相应刻度上。同时，在数轴两侧各有一条垂直参考线，用于对齐。整个图形包含一个随机化按钮，用于切换不同题目，并显示正确计数。
以上提示语为根据原始绘图命令整理而来，仅供参考。